By applying the dimensional raising maps from Refs. [1]}, [2]}, [3]} to the two dimensional first order topological superconductors in class D and class DIII, one shows that \(d-2\)  dimensional defects binding a \(\pi \) -flux in all related symmetry classes and dimensions host \(d-2\)  dimensional anomalous states. The dimensional raising maps starting from Cartan classes with a chiral antisymmetry were reviewed and applied in Appendix REF .
The dimensional raising map preserves the existence of \(d-2\)  dimensional states at point defects as long as all crystalline symmetries, if present, act trivially in the newly added dimensions. This was exemplified in Sec. REF  and was shown using a dimensional reduction scheme based on the scattering matrix in Ref. [4]}.
